Global stabilization of the unstable Reaction‐Wheel Pendulum

The paper deals with the problem of the Reaction Wheel Pendulum stabilization about unstable (inverted) position for arbitrary initial conditions. Considered mechanical system consists of a physical pendulum with a symmetric disk attached to the end of the pendulum, which is free to spin about an axis parallel to the axis of rotation of the pendulum. The disk is actuated by a DC‐motor. The coupling torque generated by the angular acceleration of the disk is used to control of the pendulum. The switching control law is proposed to swinging up the pendulum and balancing it about the inverted position. The nonlinear swinging up control law is proposed ensuring global stabilization of the pendulum about inverted position. The Energy‐based Speed‐gradient (EBSG) control scheme is used to designing the swinging‐up controller. The modification of the EBSG method is proposed to ensure attainability of the inverted position of the pendulum for all initial states of the system. The balance controller is designed on the basis of the Variable Structure Control with forced sliding mode. Numerical simulation results are presented showing achievement of the posed control goal by means of the control action of small magnitude.